"Can I please go back to war?" asks the hero of Enlisted. His name is Pete Hill (Geoff Stults). He's a hot-tempered staff sergeant who served in the Army in Afghanistan, got kicked out for punching an officer, and now finds himself reassigned Stateside alongside his two brothers (Chris Lowell and Parker Young) to "Rear D," a supply and maintenance division. That's probably a bit more jargon than you're used to seeing in a review of a new Fox sitcom, but the specificity is part of what makes Enlisted so enjoyable.

The show's creator, Kevin Biegel, comes from a military family, and a lot of the humor has a comfortably "inside" tone — like the tone you see in showbiz comedies by people who've worked in showbiz, or in school stories created by people who've worked as teachers or administrators. There are hints that M*A*S*H-like darker shadings might be unveiled later, including a moment that acknowledges that people are still being killed and wounded in two overseas conflicts and that it's not a laughing matter. But for the most part, this is a light, bouncy service comedy in the spirit of The Phil Silvers Show, Gomer Pyle, USMC, and Stripes (in a future episode, there's a competition whose grand prize is a statue of "General Murray"), It's a high jinks–heavy but psychology-driven show that wants to please a general audience while also seeming halfway credible to viewers who've served in the armed forces or know somebody who has.

On that score, Enlisted is a success. On the "Make me laugh no matter who I am" score, it's a success as well. Long sections of its first four episodes have the whip-crack comic timing of classic Simpsons, as well as the giddiness that comes from realizing that you know what has to happen next because you understand the characters as well as the characters understand each other.

Pete Hill is a brawny badass who won't stop talking about his battlefield prowess. This is his way of drowning out insecurity about being reassigned to Rear D, where he's placed in charge of training a hapless "goon platoon" full of oddballs and borderline-washouts. It's also a means of reestablishing dominance over his screwup younger brothers, Derrick (Lowell) and Randy (Young). Randy's a goofy man-child, practically a Gilligan-type, at times nearly a Lenny in Of Mice and Men–type. (He's so empathetic that he imagines the inner lives of paper targets on the shooting range.) Derrick's more self-aware but seemingly just as incapable of becoming an Army "lifer" — a goal that big brother Pete seemed well on his way to attaining when his Afghanistan outburst got him shipped back home. Turns out there was a psychological trigger for that meltdown — there's a psychological prompt for every decision on Enlisted, which distinguishes it from sitcoms that seem to come up with kooky plots and then shoehorn characters into them — and once we figure it out near the end of the pilot, it triggers a moment of unforced and dramatically earned emotion that is also rare in TV sitcoms.

I like how the major characters know each other's quirks and blind spots better than they know their own; it's true to the obliviousness of real life. "Sometimes I feel like we talk at each other," Pete tells Derrick, who ignores him and continues yammering. When Pete presses the Goon Platoon to devise a motivational logo, a private suggests, "How about you give me back the CDs you borrowed, Brian?" Sergeant Jill Perez (Angelique Cabral), who trains a rival platoon, is incapable of personalizing anyone in her group and often forgets the names of people who are currently in it, and whenever she's called on this, she just sort of blinks and keeps on talking. When the unit's big boss, Command Sergeant Major Donald Cody (Keith David), takes off the artificial foot that he lost to a land mine, it's always for shock value or rhetorical emphasis — and it never has the desired effect because everyone knows Cody is the guy who takes off his artificial foot to amp up the drama. (Cody is black, but it's a white foot, because that's the only color they had in his shoe size.)

Next week's episode, which revolves around competition for the Murray trophy for excellence in soldiering, is a kick — particularly the sublimated flirtation between Pete and Jill, which has the warring-egos sexiness that made screwball romances like His Girl Friday so pleasurable. If you have a DVR, you'll want to set it to record the January 24 episode "Prank War," a slow-building classic of one-upsmanship that's as sharp as the prank-driven episodes of M*A*S*H. The episode also gives David, one of the country's finest living character actors, a chance to unleash a comic grandiosity that's as intense as it is hilarious. I might have to make a ringtone of him growling, "Game on, nature!"

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